Hello,
When i use Proc severity and proc univariate to estimate parameters,
i have a difference between my 2 estimate parameters.
How i can resolve this problem?
I would like to have exactly the same parameter.
Exemple :
DATA Grave2;
INPUT Var1;
CARDS;
148234
17967
24066
20357
2409
93913
24879
75094
42631
50359
22077
63590
25720
57214
228177
105531
77630
62990
99790
477139
;
RUN;
/*a)Estimate parameter with proc Univariate*/
rsubmit;
proc univariate data=Grave2;
var VAR1;
histogram / gamma(theta=0);
qqplot / gamma(theta=0 alpha=est Sigma=est);
ppplot / gamma(theta=0 alpha=est Sigma=est);
histogram / lognormal(theta=0);
qqplot / lognormal(theta=0 zeta=est Sigma=est);
ppplot / gamma(theta=0 alpha=est Sigma=est);
histogram / weibull(theta=0);
qqplot / weibull(theta=0 C=est Sigma=est);
ppplot / weibull(theta=0 C=est Sigma=est);
histogram / pareto(theta=0);
qqplot / pareto(theta=0 alpha=est Sigma=est);
ppplot / pareto(theta=0 alpha=est Sigma=est);
run;
endrsubmit;
/*b) Estimate parameter with Proc severity*/
rsubmit;
proc severity data=Grave2 crit=aic covout plots=none; /* call proc on view */loss VAR1;
title "Statistique des sinistres et selection de la loi par critère AIC";
dist gamma logn weibull gpd /*Pareto donne des résultats trop differents entre severity et univariate*/;
/*dist _predefined_; Preselection de lois utilisées en réassurance*/
run;
endrsubmit;
Regards,
There are many ways to fit distributional parameters to data: method of moments, optimization of the likelihhod equation, optimization of an approximate likelihood, matching percentiles, and so forth. The estimates can also depend on the initial guess and the numerical optimization technique.
The documentation for the procedures descrbe how the parameters are estimated. The doc tor PROC SEVERITY shows how parameters are initialized and what estimation techniques are used. For example, for a gamma distribution, an APPROXIMATE MLE is formed by approximating the digamma function. This results in a fast estimation. In contrast, the UNIVARIATE procedure solves the true MLE by using the full digamma fnuction. It is slower, but more accurate.
In short, you are not going to be able to get exactly the same answers for the distributions for which SEVERITY and UNIVARIATE use different estimation methods. For distributions like the gamma, the documentation indicates that the estimates might be off by a few percentage points.
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